Crooked permutations were defined twenty years ago. It was firstly shown that they can be used to construct interesting objects in graph theory. The field of applications was extended later, since crooked functions, bijective or not, correspond to APN functions and to some optimal codes. We adopt an unified presentation, of crooked functions, explaining the connexion with partially-bent functions. We then complete some known results and propose new properties. For instance, crooked functions allow to construct sets of bent functions, or simply define some permutations.